Most polarization-sensitive photodetectors detect either linearly polarized (LP) or circularly polarized (CP) light. Here, we experimentally demonstrate a multiple-polarization photodetector based on a hybrid organic-inorganic perovskite (HOIP) metasurface, which is sensitive to both LP and CP light simultaneously. The perovskite metasurface is composed of a HOIP antenna array on a single-crystal HOIP film. Owing to the antenna anisotropy, the absorption of linearly polarized light at the metasurface depends on the polarization angle; also, due to the mirror asymmetry of the antenna elements, the metasurface is also sensitive to different circular polarizations. Polarization-dependent photocurrent responses to both LP and CP light are detected. Our results highlight the potential of perovskite metasurfaces for integrated photoelectric applications.